Trefoil knot and ad-hoc classification of elementary fields in the Standard Model

TL;DR

This paper proposes a novel model using trefoil knots to classify elementary particles, reproducing the spectrum of the Standard Model but lacking Higgs-like entities, and highlighting a new topological approach to particle classification.

Contribution

It introduces a knot-based framework for classifying elementary particles, offering a topological perspective that reproduces the particle spectrum without Higgs degrees of freedom.

Findings

Reproduces the spectrum of elementary particles using trefoil knots.

Classifies waves into 1, 3, and 8 types based on Lorentz invariance.

Does not accommodate Higgs-like degrees of freedom.

Abstract

We present an arbitrary model based on the trefoil knot to construct objects of the same spectrum as that of elementary particles. It includes `waves' and three identical sets of sources. Due to Lorentz invariance, `waves' group into 3 types of 1, 3 and 8 objects and `sources' consists of 3 identical sets of 30+2 elements, which separate into: 1 * 1 * 2 + 1 * 2 * 2 + 3 * 2 * 2 + 3 * 1 * 2 + 3 * 1 * 2 and another 1 * 1 * 2 group (which does not match classification of the Standard Model fields). On the other hand, there is no room in this construction for objects directly corresponding to Higgs-like degrees of freedom.